This study numerical investigates unsteady freeconvection in a square permeable cavity, driven by magnetohydrodynamic flow of TiO2-H2O nanofluid. The cavity features partially heated vertical walls, with adiabatic bottom and inclined upper walls, a scenario with widespread applications in fields such as heating, ventilation, and air conditioning (HVAC), electronic cooling, solar collectors, building insulation, automotive engineering, geothermal energy, and aerospace technology. The governing equations are discretized using the Marker and Cell (MAC) method, with spatial discretization achieved through the finite difference technique. A staggered grid system is employed to enhance stability and accuracy, and the resulting equations are solved iteratively to capture the unsteady behavior of the system.The study examines the range of Darcy number <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14025_Article_IEq1.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="155" /> </InlineMediaObject> <EquationSource Format="TEX">$\left( {10^{ - 1} \le {\text{Da}} \le 10^{ - 3} } \right),$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mfenced close=")" open="("> <mrow> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>≤</mo> <mtext>Da</mtext> <mo>≤</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </mrow> </mfenced> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> Rayleigh number <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14025_Article_IEq2.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="136" /> </InlineMediaObject> <EquationSource Format="TEX">$\left( {10^{3} \le {\text{Ra}} \le 10^{6} } \right),$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mfenced close=")" open="("> <mrow> <msup> <mn>10</mn> <mn>3</mn> </msup> <mo>≤</mo> <mtext>Ra</mtext> <mo>≤</mo> <msup> <mn>10</mn> <mn>6</mn> </msup> </mrow> </mfenced> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> Hartmann number <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14025_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="124" /> </InlineMediaObject> <EquationSource Format="TEX">$\left( {10 \le Ha \le 30} \right),$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mfenced close=")" open="("> <mrow> <mn>10</mn> <mo>≤</mo> <mi>H</mi> <mi>a</mi> <mo>≤</mo> <mn>30</mn> </mrow> </mfenced> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> Prandtl number <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14025_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="81" /> </InlineMediaObject> <EquationSource Format="TEX">$\left( {\Pr = 6.2} \right),$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mfenced close=")" open="("> <mrow> <mo>Pr</mo> <mo>=</mo> <mn>6.2</mn> </mrow> </mfenced> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> inclined magnetic field inclination angle <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14025_Article_IEq5.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="101" /> </InlineMediaObject> <EquationSource Format="TEX">$\left( {\gamma = \frac{\pi }{6},\frac{\pi }{4},\frac{\pi }{3}} \right),$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mfenced close=")" open="("> <mrow> <mi>γ</mi> <mo>=</mo> <mfrac> <mi>π</mi> <mn>6</mn> </mfrac> <mo>,</mo> <mfrac> <mi>π</mi> <mn>4</mn> </mfrac> <mo>,</mo> <mfrac> <mi>π</mi> <mn>3</mn> </mfrac> </mrow> </mfenced> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> heat source/sink parameter <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14025_Article_IEq6.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="102" /> </InlineMediaObject> <EquationSource Format="TEX">$\left( { - 6 \le Q \le 6} \right)$</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mrow> <mo>-</mo> <mn>6</mn> <mo>≤</mo> <mi>Q</mi> <mo>≤</mo> <mn>6</mn> </mrow> </mfenced> </math></EquationSource> </InlineEquation>. Parametric modeling explores, streamline and isotherm plots reveal rising <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14025_Article_IEq7.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">${\text{Ra}}$</EquationSource> <EquationSource Format="MATHML"><math> <mtext>Ra</mtext> </math></EquationSource> </InlineEquation> enhance heat transfer, while increased Darcy numbers intensify fluid flow and broaden temperature gradients. Larger heat source/sink parameters expand isotherm contours, amplifying convection. Validation against prior studies confirms the model's reliability and provides insights into the intricate thermal dynamics of the system.

Thermal and flow dynamics of unsteady MHD nanofluid convection in a partially heated porous cavity

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2025年3月4日

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S. Vigneshwari,
B. Reddappa,
A. Sumithra,
B. Rushi Kumar,
Hakan F. Öztop

摘要

This study numerical investigates unsteady freeconvection in a square permeable cavity, driven by magnetohydrodynamic flow of TiO₂-H₂O nanofluid. The cavity features partially heated vertical walls, with adiabatic bottom and inclined upper walls, a scenario with widespread applications in fields such as heating, ventilation, and air conditioning (HVAC), electronic cooling, solar collectors, building insulation, automotive engineering, geothermal energy, and aerospace technology. The governing equations are discretized using the Marker and Cell (MAC) method, with spatial discretization achieved through the finite difference technique. A staggered grid system is employed to enhance stability and accuracy, and the resulting equations are solved iteratively to capture the unsteady behavior of the system.The study examines the range of Darcy number $\left( {10^{ - 1} \le {\text{Da}} \le 10^{ - 3} } \right),$ $(10^{- 1} \leq Da \leq 10^{- 3}),$ Rayleigh number $\left( {10^{3} \le {\text{Ra}} \le 10^{6} } \right),$ $(10^{3} \leq Ra \leq 10^{6}),$ Hartmann number $\left( {10 \le Ha \le 30} \right),$ $(10 \leq H a \leq 30),$ Prandtl number $\left( {\Pr = 6.2} \right),$ $(Pr = 6.2),$ inclined magnetic field inclination angle $\left( {\gamma = \frac{\pi }{6},\frac{\pi }{4},\frac{\pi }{3}} \right),$ $(γ = \frac{π}{6}, \frac{π}{4}, \frac{π}{3}),$ heat source/sink parameter $\left( { - 6 \le Q \le 6} \right)$ $(- 6 \leq Q \leq 6)$ . Parametric modeling explores, streamline and isotherm plots reveal rising ${\text{Ra}}$ $Ra$ enhance heat transfer, while increased Darcy numbers intensify fluid flow and broaden temperature gradients. Larger heat source/sink parameters expand isotherm contours, amplifying convection. Validation against prior studies confirms the model's reliability and provides insights into the intricate thermal dynamics of the system.